A quarantine tank is simply a spare aquarium or container that can house new fish for a month so they can be monitored for diseases. If they develop a disease whilst in quarantine, you treat it then and there and this stops the disease getting into the main display tank. If the fish don't show any signs of disease, yo don't treat them. The only exception to this is deworming the fish. All new fish should be dewormed in quarantine. You use Praziquantel to treat tapeworm and gill flukes, and Levamisole to treat thread/ round worms.
Most people have a spare filter in the main tank and use that in the quarantine tank when they get new fish.
eg: you plan on getting some new fish tomorrow. So today you fill up the quarantine tank with water from the main display tank and some dechlorinated tap water (50/50 mix of tap and tank water). Have a thin layer of sand or gravel in the tank. Add a heater and put the spare filter in the tank. Add a couple of plastic plants and some ornaments for bottom dwellers to hide under.
The next day you go to the shop and get the new fish, bring them home and acclimatise them to the quarantine tank. The fish stay there for a month and there are no problems, they get moved into the display tank.
After the quarantine period, you wash the filter, ornaments, and quarantine tank out. Let the tank, ornaments, gravel, etc dry out and put the filter back in the main tank.
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You do water changes on the tank each week just like on a normal tank. If you get ammonia or nitrite readings you do big water changes every day until the ammonia and nitrite levels remain on 0.